Research On Phase Transition And Non Hermitian Effects In Topological Superconductors

Since the discovery of superconductivity in the early twentieth century,people’s exploration of superconductivity is always on the way.It wasn’t until the 1950s that BCS theory explained that the microscopic mechanism of superconductivity is the pairing of electrons.With the development of condensed matter physics and ultra cold atomic experimental platforms,the research on superconductor and its mechanism has attracted more and more researchers.The study of the pairing mechanism has also been developed from the s wave spin singlet pairing to the spin triplet pairing,the paring induced by particle density fluctuations,spin fluctuations,etc.So far,ten physicists have been awarded the Nobel Prize in Physics for their contributions to the field of superconductivity.Since the twenty-first century,with the discovery of more and more new superconductors,the achievement of higher and higher transition temperatures,the existing theories are becoming more and more insufficient to explain the phenomenon of superconductivity.And with the people’s more understanding of topology,the topological properties of superconducting system have also received extensive attention,especially after realizing the great parctical application potential of topological superconductors.Based on the fact that spin orbital coupling effects and transverse magnetic fields in s wave superconductivity can induce non-trivial topological states,we studied the spin exchange effect(or proximity effect)between a one-dimensional conventional s wave superconductor and a skyrmion lattice.The topological properties of the system,the corresponding topological invariants,the Majorana zero energy mode on the boundary and the corresponding bulk edge correspondence are studied,and the topological phase diagram of the system is achieved.The spin orbit coupling introduced by the spin exchange induces a topological non-trivial superconductor state in contrast to a conventional superconductor.This topological state is characterized by winding number,which is served as topological invariant of the system.And the topological phase transition is accompanied by the gap reopen process.The topological phase diagram of the system has a strong relationship with the radius of the skyrmion lattice.With a larger radius,the topological phase diagram of the system would be more complex.This work is important in understanding the spin orbit coupling effect in one-dimensional topological superconducting systems.The effect of magnetic fields in superconductors plays an important role in the research of superconductivity.We studied the superfluid phase in two-dimensional Bosonic Haldane model with on site Hubbard interaction.The system will undergo a phase transition between the uniform superfluid phase and the chiral superfluid phase driven by the next nearest neighbor hopping.Under the action of pseudo sublattice potential,particles will tend to condense on one of the sublattices,and the system will undergo a phase transition between the chiral superfluid phase and the sublattice superfluid phase.We also use the order from quantum disorder method to lift the accidental degeneracy on global phase.Then,the low-energy behavior of each phase is studied.The work is not only a generalization of the bosonic form of the Haldane model,it is also a study on the pseudo sublattice potential effect in superconductivity.In particular,it is of great significance for the exploration and realization of superconductivity in cold atomic systems.Based on the non-Bloch wave method,we studied the topological properties of a two-dimensional non-Hermitian chiral superconductor system.We demonstrate the equivalence between the generalized and original Brillouin zone of this particular system.We characterize the topological properties of the system by a two-dimensional strong topological invariant and two one-dimensional weak topological invariants,and found the physical interpretation of three topological invariants.The strong topological invariants corresponding to the boundary Majorana zero-energy mode,and the weak topological invariants correspond to the Majorana zero-energy mode in the center of the edge dislocation of the system,The corresponding bulk edge correspondence is also established.We use the flow of exceptional points to divide the generalized Brillouin zone,and use the chirality of the topological charge flow properties to define the chirality of each chart,The quantitative relationship between the change of topological invariants in the process of the phase transition and the chirality of the high symmetry points is established.The correctness of this quantitative relationship was checked under a wide range of parameter intervals.This work is a on the two-dimensional non-Hermitian system,which provides a new idea for the detection of non-Heritian topological phase transition,and is of great significance in terms of the stability of the topological boundary mode.